Carathéodory’s Theorem and the chain rule

[@akak-dg8di]

Great explanation

[@DrMcCrady]

Thank you, glad it was helpful!

[@sahilkolhe2677]

Thank you so much 🙏🙏🙏🙏🙏

[@DrMcCrady]

Glad it was helpful!

[@DiegoMathemagician]

whoa! very cool proof(s)

[@DrMcCrady]

Thanks!

[@S24W2]

Thank you, where did the x-c go near the end please?

[@DrMcCrady]

Hi! Can you give me time stamp for when it seems to disappear?

[@S24W2]

@@DrMcCrady thank you for reply, I suppose from 11:30 onwards, but I think I get it now, not 100 percent sure

[@S24W2]

@@DrMcCrady it is the (x-c) multiplied by the phi

[@DrMcCrady]

@@S24W2 in the line above there’s the expression f(x)-f(c). Then by Caratheodory’s Theorem that is the same as phi(x)(x-c). So I just substituted this expression in on the next line in place of cx)-f(c). Does that make more sense?

[@S24W2]

@@DrMcCrady thank you, yes i got that part, and I think I understand the rest, your reply is very much appreciated, thank you and great video btw

[@bishalsaha9632]

Sir on what basis we define the function ¢(x)??

[@DrMcCrady]

Hi Bishal, Under the assumption that f is define on the interval, and the assumption that f’(c) exists, the piecewise function is well defined.